Question

A board, 74 cm long is cut into three pieces such as the second board is twice as long as first board and the third is 4 cm longer than second. Find length of shorter piece

Answer 1

The shortest piece is the first piece and it is 14 cm long.

Explanation:

We have three unknowns so we need 3 equations.

Let x = the length of the first piece

Let y = the length of the second piece

Let z = the length of the third piece.

x + y + z = 74 y = 2x z = y + 4

There are a number of ways to solve this. I am going to plug in 2x for y into the first and the third equation to get:

x + y + z = 74

x + 2x + z = 74 Combine the x terms

3x + z = 74

Next, I am going to substitute 2x in for y in the third equation above.

z = y + 4

z = 2x + 4 I am going to put both variable on the left side of the equation

z - 2x = 4

I can know take the two bold equations that I have above and solve for the either x or z. I am going to solve for z. I need one of the equation to have a z and the other equation to have -z so that they will cancel one another out. I am going to multiple z - 2x = 4 all the way through by -1 to get:

z - 2x = 4

-1(z - 2x) = 4(-1)

-z +2x = -4

I am going to rearrange 3x + z = 74 so that the z term is first and add it to -z + 2x = -4

z + 3x = 74

-z + 2x = -4

5x = 70 divide both sides by 5

x = 14 This is the length of the first piece.

y = 2x

y = 2(14) = 28

y = 28 This is the length of the second piece.

z = y+4

z = 28 + 4 = 32

or

x + y + z = 74

14 + 28 + z = 74

42 + z = 74 Subtract 42 from both sides.

z = 32